That's literally an American problem. Here in the UK, it's extremely easy to set up a bank account even if you don't earn very much, or if you recently declared bankruptcy. If America wanted to help the unbanked, they have every opportunity to do so.
There are plenty of ways for the unbanked to get an account. From online banks with $0 deposit requirements, to local banks with $25minimums. While there certainly are literacy or accessibility issues, the number one cause of not having a bank account, according to FDIC surveys is not trusting banks.
The first time I tried to get a bank account as a mostly broke college student, I walked into a branch of the bank that had an agreement with my university to supply ATMs on campus. I said I wanted an account. They did everything in their power to not give me an account. Eventually, they rejected me because I had a NYS non-driver's ID card instead of a license. "We've had problems with these," they said. This bank branch was in downtown Manhattan, where roughly no one drives.
A few years after I managed to get them to give me an account, I overdrafted my checking account by a few dollars and they disabled my ATM card. After my next deposit cleared, I went back to that bank branch to get my card reinstated. They did not want to do it. The manager eventually said he could help me if I "promised I wouldn't do it again". I asked for my account to be closed instead, and I will always remember how pleased the guy seemed to be losing me as a customer.
It is not easy for everyone to get and maintain a bank account.
I just looked like someone who was not worth their time. I never did have more than $100 in the account, and dealing with me might have cost them more than they made on me since I didn't pay any fees except for the one time I overdrafted.